Annex

Data Columns Detailed

Data summary

Name	data
Number of rows	45896
Number of columns	26
_______________________
Column type frequency:
character	8
numeric	18
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
Make	0	1	3	34	0	141	0
Model	0	1	1	47	0	4762	0
Fuel.Type.1	0	1	6	17	0	6	0
Fuel.Type.2	0	1	0	11	44059	5	0
Drive	0	1	0	26	1186	8	0
Engine.Description	0	1	0	46	17031	590	0
Transmission	0	1	0	32	11	41	0
Vehicle.Class	0	1	4	34	0	34	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
ID	0	1.00	23102.11	13403.10	1.00	11474.75	23090.50	34751.25	46332.00	▇▇▇▇▇
Model.Year	0	1.00	2003.61	12.19	1984.00	1992.00	2005.00	2015.00	2023.00	▇▆▆▇▇
Estimated.Annual.Petrolum.Consumption..Barrels.	0	1.00	15.33	4.34	0.05	12.94	14.88	17.50	42.50	▁▇▃▁▁
City.MPG..Fuel.Type.1.	0	1.00	19.11	10.31	6.00	15.00	17.00	21.00	150.00	▇▁▁▁▁
Highway.MPG..Fuel.Type.1.	0	1.00	25.16	9.40	9.00	20.00	24.00	28.00	140.00	▇▁▁▁▁
Combined.MPG..Fuel.Type.1.	0	1.00	21.33	9.78	7.00	17.00	20.00	23.00	142.00	▇▁▁▁▁
City.MPG..Fuel.Type.2.	0	1.00	0.85	6.47	0.00	0.00	0.00	0.00	145.00	▇▁▁▁▁
Highway.MPG..Fuel.Type.2.	0	1.00	1.00	6.55	0.00	0.00	0.00	0.00	121.00	▇▁▁▁▁
Combined.MPG..Fuel.Type.2.	0	1.00	0.90	6.43	0.00	0.00	0.00	0.00	133.00	▇▁▁▁▁
Engine.Cylinders	487	0.99	5.71	1.77	2.00	4.00	6.00	6.00	16.00	▇▇▅▁▁
Engine.Displacement	485	0.99	3.28	1.36	0.00	2.20	3.00	4.20	8.40	▁▇▅▂▁
Time.to.Charge.EV..hours.at.120v.	0	1.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	▁▁▇▁▁
Time.to.Charge.EV..hours.at.240v.	0	1.00	0.11	1.01	0.00	0.00	0.00	0.00	15.30	▇▁▁▁▁
Range..for.EV.	0	1.00	2.36	24.97	0.00	0.00	0.00	0.00	520.00	▇▁▁▁▁
City.Range..for.EV…Fuel.Type.1.	0	1.00	1.62	20.89	0.00	0.00	0.00	0.00	520.80	▇▁▁▁▁
City.Range..for.EV…Fuel.Type.2.	0	1.00	0.17	2.73	0.00	0.00	0.00	0.00	135.28	▇▁▁▁▁
Hwy.Range..for.EV…Fuel.Type.1.	0	1.00	1.51	19.70	0.00	0.00	0.00	0.00	520.50	▇▁▁▁▁
Hwy.Range..for.EV…Fuel.Type.2.	0	1.00	0.16	2.46	0.00	0.00	0.00	0.00	114.76	▇▁▁▁▁

Data summary

The table below provides an overview of the dataset.

Summary Statistics

Variable	N	Mean	Std. Dev.	Min	Pctl. 25	Pctl. 75	Max
ID	45896	23102	13403	1	11475	34751	46332
Model.Year	45896	2004	12	1984	1992	2015	2023
Estimated.Annual.Petrolum.Consumption..Barrels.	45896	15	4.3	0.047	13	18	43
Fuel.Type.1	45896
... Diesel	1254	3%
... Electricity	484	1%
... Midgrade Gasoline	155	0%
... Natural Gas	60	0%
... Premium Gasoline	14138	31%
... Regular Gasoline	29805	65%
City.MPG..Fuel.Type.1.	45896	19	10	6	15	21	150
Highway.MPG..Fuel.Type.1.	45896	25	9.4	9	20	28	140
Combined.MPG..Fuel.Type.1.	45896	21	9.8	7	17	23	142
Fuel.Type.2	45896
...	44059	96%
... E85	1513	3%
... Electricity	296	1%
... Natural Gas	20	0%
... Propane	8	0%
City.MPG..Fuel.Type.2.	45896	0.85	6.5	0	0	0	145
Highway.MPG..Fuel.Type.2.	45896	1	6.6	0	0	0	121
Combined.MPG..Fuel.Type.2.	45896	0.9	6.4	0	0	0	133
Engine.Cylinders	45409	5.7	1.8	2	4	6	16
Engine.Displacement	45411	3.3	1.4	0	2.2	4.2	8.4
Time.to.Charge.EV..hours.at.120v.	45896	0	0	0	0	0	0
Time.to.Charge.EV..hours.at.240v.	45896	0.11	1	0	0	0	15
Range..for.EV.	45896	2.4	25	0	0	0	520
City.Range..for.EV...Fuel.Type.1.	45896	1.6	21	0	0	0	521
City.Range..for.EV...Fuel.Type.2.	45896	0.17	2.7	0	0	0	135
Hwy.Range..for.EV...Fuel.Type.1.	45896	1.5	20	0	0	0	520
Hwy.Range..for.EV...Fuel.Type.2.	45896	0.16	2.5	0	0	0	115

Data cleaned overview

Cleaned Dataset

Name	Number_of_rows	Number_of_columns	Character	Numeric	Group_variables
data_cleaned	42240	18	8	5	None

Cleaned and Reduced Dataset

Name	Number_of_rows	Number_of_columns	Character	Numeric	Group_variables
data_cleaned_reduced	42061	18	8	5	None

Eigenvalues for the Principal Components Analysis

Call:
PCA(X = data_prepared, graph = FALSE) 


Eigenvalues
                       Dim.1   Dim.2   Dim.3   Dim.4   Dim.5   Dim.6   Dim.7
Variance               4.616   3.735   2.126   1.292   1.019   0.988   0.856
% of var.             25.644  20.748  11.809   7.177   5.660   5.490   4.753
Cumulative % of var.  25.644  46.392  58.201  65.378  71.038  76.527  81.280
                       Dim.8   Dim.9  Dim.10  Dim.11  Dim.12  Dim.13  Dim.14
Variance               0.827   0.765   0.549   0.510   0.349   0.193   0.137
% of var.              4.594   4.250   3.047   2.834   1.941   1.071   0.759
Cumulative % of var.  85.875  90.124  93.172  96.005  97.946  99.017  99.777
                      Dim.15  Dim.16  Dim.17  Dim.18
Variance               0.027   0.008   0.003   0.002
% of var.              0.150   0.045   0.018   0.011
Cumulative % of var.  99.926  99.971  99.989 100.000

Individuals (the 10 first)
                                 Dist    Dim.1    ctr   cos2    Dim.2    ctr
1                            |  3.334 | -1.087  0.001  0.106 |  0.065  0.000
2                            |  3.387 | -0.907  0.000  0.072 | -0.079  0.000
3                            |  3.522 | -1.153  0.001  0.107 | -0.031  0.000
4                            |  2.761 | -1.068  0.001  0.150 |  0.012  0.000
5                            |  2.713 | -0.991  0.001  0.133 | -0.022  0.000
6                            |  2.713 | -0.991  0.001  0.133 | -0.022  0.000
7                            |  2.847 | -1.039  0.001  0.133 | -0.066  0.000
8                            |  2.876 | -1.151  0.001  0.160 | -0.019  0.000
9                            |  4.850 | -1.810  0.002  0.139 |  0.346  0.000
10                           |  3.313 | -1.686  0.001  0.259 |  0.231  0.000
                               cos2    Dim.3    ctr   cos2  
1                             0.000 |  0.018  0.000  0.000 |
2                             0.001 |  2.589  0.007  0.584 |
3                             0.000 |  2.603  0.008  0.546 |
4                             0.000 |  0.658  0.000  0.057 |
5                             0.000 |  0.609  0.000  0.050 |
6                             0.000 |  0.609  0.000  0.050 |
7                             0.001 |  0.490  0.000  0.030 |
8                             0.000 |  0.546  0.000  0.036 |
9                             0.005 | -0.005  0.000  0.000 |
10                            0.005 |  1.551  0.003  0.219 |

Variables (the 10 first)
                                Dim.1    ctr   cos2    Dim.2    ctr   cos2  
make                         |  0.106  0.242  0.011 | -0.092  0.229  0.009 |
model_year                   |  0.347  2.605  0.120 |  0.032  0.028  0.001 |
vehicle_class                | -0.141  0.428  0.020 |  0.051  0.071  0.003 |
drive                        | -0.038  0.031  0.001 |  0.003  0.000  0.000 |
engine_cylinders             |  0.077  0.130  0.006 | -0.073  0.141  0.005 |
engine_displacement          |  0.125  0.338  0.016 | -0.104  0.292  0.011 |
transmission                 | -0.498  5.376  0.248 |  0.069  0.128  0.005 |
fuel_type_1                  | -0.419  3.802  0.175 |  0.223  1.328  0.050 |
city_mpg_fuel_type_1         |  0.837 15.173  0.700 | -0.308  2.532  0.095 |
highway_mpg_fuel_type_1      |  0.800 13.860  0.640 | -0.313  2.630  0.098 |
                              Dim.3    ctr   cos2  
make                         -0.472 10.475  0.223 |
model_year                   -0.120  0.679  0.014 |
vehicle_class                 0.474 10.568  0.225 |
drive                         0.158  1.172  0.025 |
engine_cylinders              0.755 26.797  0.570 |
engine_displacement           0.851 34.040  0.724 |
transmission                 -0.018  0.016  0.000 |
fuel_type_1                  -0.170  1.358  0.029 |
city_mpg_fuel_type_1         -0.242  2.753  0.059 |
highway_mpg_fuel_type_1      -0.351  5.790  0.123 |

3D Biplot for 6 clusters

Warning in PCA(data_prepared, graph = FALSE): Missing values are imputed by the
mean of the variable: you should use the imputePCA function of the missMDA
package

After looking at the silhouette plot in the unsupervised learning part, we decided to provide a 3D biplot for 6 clusters, as we can also see in the elbow plot that 6 seem to be optimal in a way. In this biplot, we can observe that it is possible to divide into 6 clusters. When comparing it to the 3D biplot in the ‘results_unsupervised_learning’ part, we clearly notice that cluster 2 could be divided into four smaller clusters, which indicates heterogeneity in this cluster when using only 3 clusters. However, with 6 clusters in hand, it is more difficult to interpret the 4 distinct clusters. In addition to that, it explains the second elbow in the elbow method: at 3 clusters, we obtained optimality, but we get another steep curve between cluster 5 and 6, meaning that selecting 4 or 5 clusters would not be too much of a benefit, but adding a 6th cluster could be worth capturing. Stopping at 3 cluster still is significant for us and it makes our clustering anaylsis more interpretable than 6, that’s why we selected only 3 clusters for our analysis.